Theoretical and Experimental Studies of Slender Vortex Filaments

Abstract

We show how theoretical analysis and experimental investigation complement each other in the study of the dynamics of slender vortex filaments. The asymptotic solution of a single filament requires the initial data of the shape of the centerline and the core structure. The latter is usually not available from experimental data. When the viscous diffusion time td of the core is of the order of the duration t* of the experiment, we can define the contribution of the core structure to the filament velocity by a finite number of parameters, which can then be determined by comparing the theoretical predictions of the motion of the centerline with the experimental data. These parameters, in turn, calibrate the single vortex generator in the experimental set up by defining the moments of the initial core structure. In the inviscid limit, where t* &unknown; td, we derive the formulas for the contributions of the the core structure to the filament velocity and show that they depend only on two initial data. The analytical solution can then be used to model the interaction of filaments with or without boundaries or interfaces, and compare with the experimental data.